Linear Substitution Method

Introduction to linear substitution method:          

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Linear equations can have one or more variables.

A common form of a linear equation in the two variables xy is

The example and practice problems are given below to solve linear equation by substitution method.

Example Problems for Solving Linear Equations by Substitution Method:
Example 1:

Solve the following system of linear equation by substitution method.

3x + 2y = 6

y =  8 - 2x

Solution:

Step 1: Given equations

3x + 2y = 6 ---------------> (1)

y = 8 - 2x   ---------------> (2)

Step 2: Substitute the equation (2) in equation (1) in the place of y. So,

3x + 2y = 6            

3x + 2(8 - 2x) = 6

Step 3: Solve the above equation for x

Multiply the inner terms with (8 - 2x) with 2,

3x + 16 - 4x = 6

- x + 16 = 6

Subtract 16 on both sides to cancel 16 in left hand side,

- x + 16 - 16 = 6 - 16

- x = - 10

x = 10

Step 4: Substitute x = 10 in equation (2)

y = 8 - 2x

y = 8 - 2(10)

y = 8 - 20

y = - 12

Step 5: Solution

x = 10

y = - 12

Example 2:

Solve the following system of linear equation by substitution method.

4x + 3y = 6

y = 8 - 3x

Solution:

Step 1: Given equations

4x + 3y = 6 ---------------> (1)

y = 8 - 3x   ---------------> (2)

Step 2: Substitute the equation (2) in equation (1) in the place of y. So,

4x + 3y = 6

4x + 3(8 - 3x) = 6

Step 3: Solve the above equation for x

Multiply the inner terms with (8 - 3x) with 3,

4x + 24 - 9x = 6

- 5x + 24 = 6

Subtract 24 on both sides to cancel 24 in left hand side,

- 5x + 24 -24 = 6 - 24

- 5x = - 18

Divide by 5 on both sides,

- 5x/5 = - 18/5

- x = - 3.6

x = 3.6

Step 4: Substitute x = 3.6 in equation (2)

y = 8 - 3x

y = 8 - 3(3.6)

y = 8 - 10.8

y = - 2.8

Step 5: Solution

x = 3.60

y = - 2.80

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Practice Problems for Solving Linear Equations by Substitution Method:

1) Solve the following system of linear equation by substitution method.

2x + y = 6

y = 8 - 3x

2) Solve the following system of linear equation by substitution method.

6x + 4y = 6

2y = 9 - 4x

Solutions:

1) x = 2 ; y = 2

2) x = 6 ; y =- 7.5

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